SynchronoGeometry: Cosmic Acceleration from Local Temporal Asynchrony

This paper introduces SynchronoGeometry, a geometric framework that explains the observed accelerated expansion of the universe without invoking dark energy. The model is based on the idea that time is not globally uniform but varies locally, represented by a dynamical scalar field )T(xμ) at each spacetime point. This "temporal asynchrony" leads to a local rescaling of the metric, whose cumulative effect mimics cosmic acceleration. Starting from an augmented Einstein-Hilbert action, we derive modified Friedmann equations that yield an effective late-time acceleration. The framework makes concrete, falsifiable predictions: it predicts small, redshift-dependent deviations in the Hubble parameter H(z) and the effective equation-of-state parameter w(z), at the level of (10−3)O(10−3) for ≲2z≲2. These deviations are within the reach of upcoming cosmological surveys such as Euclid, DESI, and JWST. The absence of such deviations would rule out the minimal coupling formulation presented here, providing a clear empirical test to distinguish SynchronoGeometry from the standard ΛCDM model and other phenomenological alternatives.